Loughborough University
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Simulation of all-scale atmospheric dynamics on unstructured meshes

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journal contribution
posted on 2016-11-18, 10:56 authored by Piotr K. Smolarkiewicz, Joanna SzmelterJoanna Szmelter, Feng Xiao
The advance of massively parallel computing in the nineteen nineties and beyond encouraged finer grid intervals in numerical weather-prediction models. This has improved resolution of weather systems and enhanced the accuracy of forecasts, while setting the trend for development of unified all-scale atmospheric models. This paper first outlines the historical background to a wide range of numerical methods advanced in the process. Next, the trend is illustrated with a technical review of a versatile nonoscillatory forward-in-time finite-volume (NFTFV) approach, proven effective in simulations of atmospheric flows from small-scale dynamics to global circulations and climate. The outlined approach exploits the synergy of two specific ingredients: the MPDATA methods for the simulation of fluid flows based on the sign-preserving properties of upstream differencing; and the flexible finite-volume median-dual unstructured-mesh discretisation of the spatial differential operators comprising PDEs of atmospheric dynamics. The paper consolidates the concepts leading to a family of generalised nonhydrostatic NFTFV flow solvers that include soundproof PDEs of incompressible Boussinesq, anelastic and pseudo-incompressible systems, common in large-eddy simulation of small- and meso-scale dynamics, as well as all-scale compressible Euler equations. Such a framework naturally extends predictive skills of large-eddy simulation to the global atmosphere, providing a bottom-up alternative to the reverse approach pursued in the weather-prediction models. Theoretical considerations are substantiated by calculations attesting to the versatility and efficacy of the NFTFV approach. Some prospective developments are also discussed.


This work was supported by the funding received from the European Research Council under the European Union's Seventh Framework Programme (FP7/2012/ERC Grant agreement no. 320375), and from the ESCAPE project; ESCAPE is funded by the European Commission under the Horizon 2020 Programme—grant agreement 671627.



  • Mechanical, Electrical and Manufacturing Engineering

Published in

Journal of Computational Physics




267 - 287


SMOLARKIEWICZ, P.K., SZMELTER, J. and XIAO, F., 2016. Simulation of all-scale atmospheric dynamics on unstructured meshes. Journal of Computational Physics, 322, pp. 267-287.


© Elsevier


  • AM (Accepted Manuscript)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

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This paper was accepted for publication in the journal Journal of Computational Physics and the definitive published version is available at http://dx.doi.org/10.1016/j.jcp.2016.06.048




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